We proceed by comparing the theoretical prediction with the experimentally
determined \( W\)  boson mass and insist on agreement at the 2\( \sigma \) 
level. The empirical and SM-predicted values of \(M_W\)  are obtained from the Particle Data Group
[1]}. For
the experimentally measured \( M_W \) , we use the current world average
(prior to the 2022 CDF measurement), \( M_W^{\text{exp}} = 80.377 \pm 0.012\) 
GeV, whereas the SM prediction stands at \( M_W^{\text{th} }= 80.356 \pm 0.006\)  GeV. Combining the two errors in quadrature, we use
eq. REF  to obtain a \( U(1)_{B_3-L_2}\)  model prediction for the mass of the
\( W \)  boson and require that the predicted and measured values disagree by
less than \( 2\sigma \) . This constraint corresponds to the yellow region in
figure REF  and is the most stringent for
\(0.5<m_\vartheta /\text{~TeV}<5\) .
<FIGURE><FIGURE>